Chapter 10: Q49E (page 469)
In Figure 10.24, the band n = 1 ends at , while in Figure 10.27 it ends at. Are these compatible? If so, how?
It is proved that two ends are compatible.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Question: The interatomic potential energy in a diatomic molecule (Figure 10.16) has many features: a minimum energy, an equilibrium separation a curvature and so on. (a) Upon what features do rotational energy levels depend? (b) Upon what features do the vibration levels depend?
By expanding an arbitrary in a power series about a local minimum assumed to be at , prove that the effective spring constant is given by equation .
As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice can be treated as a one-electron atom, in which the extra electron orbits a net positive charge of 1. Because this "atom" is not in free space, however, the permitivity of free space, . must be replaced by , where is the dielectric constant of the surrounding material. The hydrogen atom ground-state energies would thus become
Given for silicon, how much energy is needed to free a donor electron in its ground state? (Actually. the effective mass of the donor electron is less than , so this prediction is somewhat high.)
Why should magnesium form a metallic solid?
Question:In Chapter 4. we learned that the uncertainty principle is a powerful tool. Here we use it to estimate the size of a Cooper pair from its binding energy. Due to their phonon-borne attraction, each electron in a pair (if not the pair's center of mass) has changing momentum and kinetic energy. Simple differentiation will relate uncertainty in kinetic energy to uncertainty in momentum, and a rough numerical measure of the uncertainty in the kinetic energy is the Cooper-pair binding energy. Obtain a rough estimate of the physical extent of the electron's (unknown!) wave function. In addition to the binding energy, you will need to know the Fermi energy. (As noted in Section 10.9, each electron in the pair has an energy of about EF.) Use 10-3 eV and 9.4 eV, respectively, values appropriate for indium.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
